Answer : The correct option is, (D) 89.39 KJ/mole
Explanation :
First we have to calculate the moles of HCl and NaOH.
![\text{Moles of HCl}=\text{Concentration of HCl}\times \text{Volume of solution}=2.6mole/L\times 0.137L=0.3562mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20HCl%7D%3D%5Ctext%7BConcentration%20of%20HCl%7D%5Ctimes%20%5Ctext%7BVolume%20of%20solution%7D%3D2.6mole%2FL%5Ctimes%200.137L%3D0.3562mole)
![\text{Moles of NaOH}=\text{Concentration of NaOH}\times \text{Volume of solution}=2.6mole/L\times 0.137L=0.3562mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20NaOH%7D%3D%5Ctext%7BConcentration%20of%20NaOH%7D%5Ctimes%20%5Ctext%7BVolume%20of%20solution%7D%3D2.6mole%2FL%5Ctimes%200.137L%3D0.3562mole)
The balanced chemical reaction will be,
![HCl+NaOH\rightarrow NaCl+H_2O](https://tex.z-dn.net/?f=HCl%2BNaOH%5Crightarrow%20NaCl%2BH_2O)
From the balanced reaction we conclude that,
As, 1 mole of HCl neutralizes by 1 mole of NaOH
So, 0.3562 mole of HCl neutralizes by 0.3562 mole of NaOH
Thus, the number of neutralized moles = 0.3562 mole
Now we have to calculate the mass of water.
As we know that the density of water is 1 g/ml. So, the mass of water will be:
The volume of water = ![137ml+137ml=274ml](https://tex.z-dn.net/?f=137ml%2B137ml%3D274ml)
![\text{Mass of water}=\text{Density of water}\times \text{Volume of water}=1g/ml\times 274ml=274g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D%5Ctext%7BDensity%20of%20water%7D%5Ctimes%20%5Ctext%7BVolume%20of%20water%7D%3D1g%2Fml%5Ctimes%20274ml%3D274g)
Now we have to calculate the heat absorbed during the reaction.
![q=m\times c\times (T_{final}-T_{initial})](https://tex.z-dn.net/?f=q%3Dm%5Ctimes%20c%5Ctimes%20%28T_%7Bfinal%7D-T_%7Binitial%7D%29)
where,
q = heat absorbed = ?
= specific heat of water = ![4.18J/g^oC](https://tex.z-dn.net/?f=4.18J%2Fg%5EoC)
m = mass of water = 274 g
= final temperature of water = 325.8 K
= initial temperature of metal = 298 K
Now put all the given values in the above formula, we get:
![q=274g\times 4.18J/g^oC\times (325.8-298)K](https://tex.z-dn.net/?f=q%3D274g%5Ctimes%204.18J%2Fg%5EoC%5Ctimes%20%28325.8-298%29K)
![q=31839.896J=31.84KJ](https://tex.z-dn.net/?f=q%3D31839.896J%3D31.84KJ)
Thus, the heat released during the neutralization = -31.84 KJ
Now we have to calculate the enthalpy of neutralization.
![\Delta H=\frac{q}{n}](https://tex.z-dn.net/?f=%5CDelta%20H%3D%5Cfrac%7Bq%7D%7Bn%7D)
where,
= enthalpy of neutralization = ?
q = heat released = -31.84 KJ
n = number of moles used in neutralization = 0.3562 mole
![\Delta H=\frac{-31.84KJ}{0.3562mole}=-89.39KJ/mole](https://tex.z-dn.net/?f=%5CDelta%20H%3D%5Cfrac%7B-31.84KJ%7D%7B0.3562mole%7D%3D-89.39KJ%2Fmole)
The negative sign indicate the heat released during the reaction.
Therefore, the enthalpy of neutralization is, 89.39 KJ/mole